def step()

in timm/optim/adafactor.py [0:0]


    def step(self, closure=None):
        """Performs a single optimization step.
        Arguments:
            closure (callable, optional): A closure that reevaluates the model and returns the loss.
        """
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad
                if grad.dtype in {torch.float16, torch.bfloat16}:
                    grad = grad.float()
                if grad.is_sparse:
                    raise RuntimeError('Adafactor does not support sparse gradients.')

                state = self.state[p]

                factored_dims, use_first_moment = self._get_options(
                    group,
                    grad.shape,
                    min_size_to_factor=group['min_dim_size_to_factor'],
                )
                # State Initialization
                if len(state) == 0:
                    state['step'] = 0

                    if use_first_moment:
                        # Exponential moving average of gradient values
                        state['exp_avg'] = torch.zeros_like(grad)
                    if factored_dims is not None:
                        dim_col, dim_row = factored_dims
                        def _remove_dim(shape, dim):
                            return shape[:dim] + shape[dim + 1:]
                        state['exp_avg_sq_row'] = torch.zeros(_remove_dim(grad.shape, dim_row)).to(grad)
                        state['exp_avg_sq_col'] = torch.zeros(_remove_dim(grad.shape, dim_col)).to(grad)
                    else:
                        state['exp_avg_sq'] = torch.zeros_like(grad)

                    state['RMS'] = 0
                else:
                    if use_first_moment:
                        state['exp_avg'] = state['exp_avg'].to(grad)
                    if factored_dims is not None:
                        state['exp_avg_sq_row'] = state['exp_avg_sq_row'].to(grad)
                        state['exp_avg_sq_col'] = state['exp_avg_sq_col'].to(grad)
                    else:
                        state['exp_avg_sq'] = state['exp_avg_sq'].to(grad)

                p_fp32 = p
                if p.dtype in {torch.float16, torch.bfloat16}:
                    p_fp32 = p_fp32.float()

                state['step'] += 1
                state['RMS'] = self._rms(p_fp32)
                lr_t = self._get_lr(group, state)

                beta2t = 1.0 - math.pow(state['step'], group['decay_rate'])
                update = grad ** 2 + group['eps']
                if factored_dims is not None:
                    dim_col, dim_row = factored_dims
                    exp_avg_sq_row = state['exp_avg_sq_row']
                    exp_avg_sq_col = state['exp_avg_sq_col']

                    exp_avg_sq_row.mul_(beta2t).add_(update.mean(dim=dim_row), alpha=1.0 - beta2t)
                    exp_avg_sq_col.mul_(beta2t).add_(update.mean(dim=dim_col), alpha=1.0 - beta2t)

                    # Approximation of exponential moving average of square of gradient
                    update = self._approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col, dim_col, dim_row)
                    update.mul_(grad)
                else:
                    exp_avg_sq = state['exp_avg_sq']

                    exp_avg_sq.mul_(beta2t).add_(update, alpha=1.0 - beta2t)
                    update = exp_avg_sq.rsqrt().mul_(grad)

                update.div_((self._rms(update) / group['clip_threshold']).clamp_(min=1.0))
                update.mul_(lr_t)

                if use_first_moment:
                    exp_avg = state['exp_avg']
                    exp_avg.mul_(group['beta1']).add_(update, alpha=1 - group['beta1'])
                    if group['caution']:
                        # Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085
                        mask = (exp_avg * grad > 0).to(grad.dtype)
                        mask.div_(mask.mean().clamp_(min=1e-3))
                        update = exp_avg * mask
                    else:
                        update = exp_avg

                if group['weight_decay'] != 0:
                    p_fp32.add_(p_fp32, alpha=-group['weight_decay'] * lr_t)

                p_fp32.add_(-update)
                if p.dtype in {torch.float16, torch.bfloat16}:
                    p.copy_(p_fp32)

        return loss